Port number has to be between 1024 and 65535

FTP Anmeldung fehlgeschlagen Konnte Verzeichnisinhalt nicht abrufen Port number has to be between 1024 and 65535

What is the problem?

I guess this is the problem ;-) .

i.e. is there a way to access portnumbers > 65535? (There seem to be OSes that support these.)

AFAIK, port number is 2 byte in TCP protocol:
https://en.wikipedia.org/wiki/Transmission_Control_Protocol#TCP_ports

You are right (of course ;-) )
Like other people, I was misled by the fact that esoteric port numbers appear in /etc/services of esoteric OSes. Nameley AIX.

I googled this conversation, that clarified my error:
https://www.unix.com/aix/110931-tcp-port-70000-aix-6-1-surely-higher-than-allowed-maximum.html